In this study, we report that quantum quasi-cyclic low-density parity-check codes decoded via joint belief propagation (BP) exhibit steep error-rate curves, despite the presence of error floors. To the best of our knowledge, this is the first observation of such threshold-like behavior for quantum codes with non-vanishing coding rate, excluding those decoded with non-binary BP decoders. Moreover, we find that dominant error events contributing to the error floor typically involve only a small number of bits. These findings suggest that the error floor is caused by trapping sets -- specific subgraph structures in the Tanner graph -- and indicate that identifying and avoiding such structures may lead to further reduction of the error floor.

翻译：本研究报道，通过联合置信传播译码的量子准循环低密度奇偶校验码展现出陡峭的误码率曲线，尽管存在错误平层现象。据我们所知，这是首次在具有非零编码率的量子码中观察到此类阈值行为（使用非二进制BP译码器的情形除外）。此外，我们发现导致错误平层的主要错误事件通常仅涉及少量比特。这些结果表明错误平层是由陷阱集——即Tanner图中的特定子图结构——所引起，并表明识别和避免此类结构可能进一步降低错误平层。